\(\dfrac{1}{100}\)

\(\frac{5^4.20^4}{25^5.4^5}=\frac{5^4.\left(4.5\right)^4}{\left(5.5\right)^5.4^5}=\frac{5^4.4^4.5^4}{5^5.5^5.4^5}=\frac{5^8.4^4}{5^8.5^2.4^4.4}=\frac{1}{5^2.4}=\frac{1}{100}\)

\(\frac{5^4\cdot20^4}{25^5\cdot4^5}=\frac{5^4\cdot5^4\cdot4^4}{5^5\cdot5^5\cdot4^5}=\frac{1}{100}\)

Đề bài là gì vậy ( rút gọn hả?)

\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{25^2\left(5.4\right)^4}{25^5.4^5}=\dfrac{1.5^4.4^4}{25^3.4^5}=\dfrac{25^2.1}{25^3.4}=\dfrac{1}{25.4}=\dfrac{1}{100}\)

\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.\left(5.4\right)^4}{\left(5^2\right)^5.4^5}=\dfrac{5^4.5^4.4^4}{5^{10}.4^5}=\dfrac{5^8.4^8}{5^{10}.4^5}=\dfrac{1.1}{5^2.4}=\dfrac{1}{100}\)

=\(\frac{100^4}{100^5}=100^{-1}=\frac{1}{100}\)

\(\frac{5^4.20^4}{25^5.4^5}=\frac{\left(5.20\right)^4}{\left(25.4\right)^5}=\frac{100^4}{100^5}=100^{-1}=\frac{1}{100}\)

\(\frac{5^4.20^4}{25^5.4^5}=\frac{5^4.\left(5.4\right)^4}{\left(5^2\right)^5.4^5}=\frac{5^4.5^4.4^4}{5^{10}.4^5}=\frac{5^{16}.4^4}{5^{10}.4^5}\)=\(\frac{5^6}{4}\)=\(\frac{3125}{4}\)

ủng hộ nha

\(\frac{5^4.20^4}{25^5.4^5}=\frac{5^4\left(1.15^4\right)}{\left(19^5.1\right).4^5}=\frac{5^4.15^4}{19^5.4^5}\)

\(\frac{5^4.20^4}{25^5.4^5}=\frac{\left(5.20\right)^4}{\left(25.4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}.\)

Chúc bạn học tốt!

Ta có:

\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.5^4.4^4}{\left(5^2\right)^5.4^5}=\dfrac{5^8.4^4}{5^{10}.4^5}=\dfrac{1}{5^2.4}=\dfrac{1}{25.4}=\dfrac{1}{100}=0,01\)

\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.\left(4.5\right)^4}{\left(5.5\right)^5.4^5}=\dfrac{5^4.4^4.5^4}{5^5.5^5.4^5}=\dfrac{1}{5.5.4}=\dfrac{1}{100}\)

\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.\left(5.4\right)^4}{\left(5^2\right)^5.4^5}=\dfrac{5^4.5^4.4^4}{5^{10}.4^5}=\dfrac{5^8.4^4}{5^8.5^2.4.4^4}=\dfrac{1}{100}\)